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Lecture 2

Lecture 2. Discrete Random Variables Section 2.1-2.4. Definition. Each observation of an experiment is a random variable . (e.g. X) The set of possible values of a random variable is called the range of a random variable. (e.g. S X ). A random variable can be a function of the observation.

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Lecture 2

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  1. Lecture 2 Discrete Random Variables Section 2.1-2.4

  2. Definition • Each observation of an experiment is a random variable. (e.g. X) • The set of possible values of a random variable is called the range of a random variable. (e.g. SX)

  3. A random variable can be a function of the observation.

  4. A random variable can be a function of another random variable

  5. English translation: {X=x} emphasizes the idea that there is a set of sample points s within S (the sample space) for which X(s)=x.

  6. Probability Mass Function

  7. Probability Mass Function

  8. Families of Discrete Random Variables • Bernoulli Random Variable • Geometric Random Variable • Binomial Random Variable • Pascal Random Variable • Discrete Uniform Random Variable (Not Covered) • Poisson Random Variable

  9. Bernoulli Random Variable

  10. Examples of a Bernoulli Random Variable (1)

  11. bernoullipmf(p,x)

  12. Geometric Random Variable

  13. Geometric RV Example (1)

  14. geometricpmf(p,x)

  15. Binomial Random Variable

  16. Binomial RV Example (1)

  17. binomialpmf(n,p,x)

  18. Pascal Random Variable

  19. Pascal Random Variable Example

  20. Pascalpmf(k,p,x)

  21. Poisson Random Variable

  22. An Example of Poisson Random Variable

  23. poinsonpmf(alpha,x)

  24. An Example of Poisson Random Variable

  25. An Example of Poisson Random Variable

  26. An Example of Poisson Random Variable

  27. CDF

  28. CDF Example

  29. geometricdf(p,x) What is the probability that Y is greater than 3?

  30. poissoncdf(alpha,x) What is the probability that the switching office receives more than 2 calls, but less than 10 calls?

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